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Outcomes of interestA total of 1000 datasets were generated for each of the 24 settings. The generated data were subsequently analyzed by fitting Model (15.1) in SAS. Two different parameterizations for the D matrix were considered. First, a completely general (unstructured; UN) D matrix that is parameterized directly in terms of variances and covariances. Second, a nondiagonal factoranalytic structure with 4 factors (FA0(4)). The latter structure specifies a Cholesky root parameterization for the 4 x 4 unstructured blocks in D. This leads to a substantial simplification of the optimization problem, i.e., the problem now changes from a constrained one to an unconstrained one. The FA0(4) structure has f (2# — q + 1) covariance parameters, where q refers to the number of factors and t is the dimension of the matrix. In the present setting, the FA0(4) structure thus has a total of 10 parameters. These parameters are used to compute the components in D, i.e., the (i, j)^{th} element of D is computed as . The Cholesky root parameterization ensures that D (and Vi) is positivedefinite during the entire estimation process (West et al., 2007). The key outcome of interest in the simulations was model convergence. Three model convergence categories were distinguished: (i) proper convergence, i.e., the model converged and the variancecovariance matrix of the random effects (D) and the final Hessian (H), used to compute the standard errors of the covariance parameters, were positivedefinite (PD); (ii) the model converged but D or H was not PD; and finally, (iii) divergence. 
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